For the storage and transmission of black and white images, such images are raster scanned and then represented by a matrix of black and white picture elements.
For most printed, typewritten or even handwritten documents, the greater portion of an image of such a document is white (e.g., the space between print lines), and a redundancy reduction is well possible. Methods for such redundance reduction are already known, e.g. from the following publications: H. S. Hou: "Digital Document Processing", pp. 124, John Wiley & Sons, New York 1983.--G. G. Landon: "An Introduction to Arithmetic Coding", IBM. J. Res. Develop. Vol. 28, No. 2, March 1984, pp. 135-149. The amount of data that has to be stored or transmitted for such images can thus be reduced significantly.
A problem with such redundancy reduction procedures is the fact that in certain situations, e.g., if documents were copied several times in sequence, if low quality copying was used, or if a document was transmitted already through a noisy channel, there exists "noise" in the documents which consists of small black spots. As the redundancy reduction process cannot recognize whether a black spot is actual data or noise, it will encode also the noise spots which will result in a heavy degradation of the redundancy reduction.
It is therefore desirable to remove the noise from black and white images after scanning and prior to any further processing.
Some procedures for noise cleaning or removal in images were disclosed in the following publications:
A. Rosenfeld, C. M. Park: "Noise Cleaning in Digital Pictures", EASCON '69 Record, pp. 264-273.--W. K. Pratt: "Digital Image Processing", John Wiley & Sons, New York 1978; Chapter 12.3 "Noise Cleaning" (pp. 319-321) and Chapter 12.6 "Median Filter" (pp. 330-333).--A. Rosenfeld, A. C. Kak: "Digital Picture Processing", 2nd Edition, Vol. 1, Academic Press, New York 1982; Chapter 6.4 "Smoothing" (pp. 250-264).
The noise removal methods described in these papers either use a contracting (shrinking) and reexpanding procedure during which small black areas vanish (they do not reappear during the expansion), or they replace the value of a picture element by the average or median value of its neighborhood picture elements so that black spots close to white areas may vanish.
Each of these noise cleaning methods requires a large amount of computing and processing. Furthermore, they tend to degrade the images because they also change thin lines and erode edges which should remain unmodified in the picture, so that noiseless images may have a reduced quality after processing by these procedures.